Answer:
d
Explanation:
Lets look at V which is at (2,-4).
We will also look at it's image V' which is at (-2,-1).
Let's go through the choices:
a. translation left 4 units and down 1 unit reflection x axis
Translating V left 4 and down 1 would give us (2-4,-4-1)
(-2,-5)
Reflecting that across the x-axis would give us
(-2,5).
So this is not (-2,-1) so let's move on...
b. translation left 2 units and up 2 units reflection line x=1
Translating V left 2 and up 2 gives us
(2-2,-4+2)
(0,-2)
Now reflecting this over x=1 gives us
(2,-2). ( Imagine this x=1 which is verical going right smack between points (0,-2) and (2,-2).)
We still did not reach our goal image.
c. translation left 2 units up and up 3 units reflection y axis
Starting at V(2,-4) and moving left 2 & up 3 gives (2-2,-4+3)=(0,-1).
Now reflecting this over the vertical axis, the y-axis, gives us (0,-1).
So we did not reach our (-2,-1) point yet.
d. translation left 2 units and 3 units reflection line x=-1.
Starting at (2,-4) then moving left 2 and up 3 gives us (2-2,-4+3)=(0,-1).
Now we are reflecting over x=-1 which means we want to choose a point on the side making x=-1 the middle. Thuis point on the other side of (0,-1) of x=-1 would be (-2,-1) which is the goal.